For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and taking inverses. Thinking of a matrix as given by n^2 coordinate functions, the set of matrices is identified with R^(n^2).
determinant | field | general orthogonal group | group | Laplacian | Lie algebra | Lie group | Lie-type group | linear algebraic group | orthogonal group representations | orthogonal matrix | orthogonal transformation | orthonormal basis | projective general orthogonal group | projective special orthogonal group | Riemannian metric | special orthogonal group | unitary group | vector space
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